I think it depends on a lot of things but most likely in this case I would let the deer walk off and move to then take the shot. Of course I don't know your stand set up so you may be able to let him walk 50 yards then move or he may be gone in 20yards into a thicket so its hard to answer for sure.
Usually at the point when "I heard a deer walking towards me" I will usually stand up if I think where the direction they are coming will present a problem for my shot. At the same time I usually go a minimum of 25' up in a tree so I can move a bit easier without being seen then if I was in a 15' stand.
Again though there are a ton of reasons/combinations without seeing your exact set up that it would be hard to answer. However I doubt I would take a left handed shot just because Im not comfortable taking them. If someone is good at shooting either way by all means go for it.